John and Beth each bought a used car at a purchase price of $12,000.

Question

John and Beth each bought a used car at a purchase price of $12,000. John paid a sales tax of j percent on the purchase price of the car that he bought, and Beth paid a sales tax of k percent on the purchase price of the car that she bought. If j > k, how much more did John pay in sales tax then Beth Paid?

(1) j is 3 more than k

(2) j is  \frac{8}{5}  of k.

Kinshook · Accepted Answer

andreaff877 
Given: John and Beth each bought a used car at a purchase price of $12,000. John paid a sales tax of j percent on the purchase price of the car that he bought, and Beth paid a sales tax of k percent on the purchase price of the car that she bought.
Asked: If j > k, how much more did John pay in sales tax then Beth Paid?

Sales tax paid by John = $12000 * j%
Sales tax paid by Beth = $12000 * k%

The amount John paid more in sales tax then Beth Paid = $12000 (j%-k%) = $120(j-k)

(1) j is 3 more than k
The amount John paid more in sales tax then Beth Paid  = $120(j-k) = $120*3 = $360
SUFFICIENT

(2) j is  \frac{8}{5}  of k. j = 8k/5
j-k = 8k/5 - k = 3k/5
The amount John paid more in sales tax then Beth Paid  = $120(j-k) = $120*3k/5 = $360k/5
Since absolute values of j or k are unknown
NOT SUFFICIENT

IMO A

egmat · Answer

A simple question with pretty solid learnings that if applied can prevent you from making mistakes.

Watch the solution to extract the learnings.
 https://www.youtube.com/watch?v=JUtNrm8zIn0

Learning:  Translate correctly to determine if the quantity being asked is the difference or the factor.

HarshaBujji · Answer

IMO A,

j=k+3;

Hence diff is 3./100(12000) ==> Using stmt 1 we can solve it.

j=8/5k; diff 0.6k(120000) this is a variable we cannot solve using stmt 2.

Hence A

RobertVericPrep · Answer

Let's start off by writing two equations reflecting the total amount of sales tax that each person paid when purchasing the car.

Let John’s “sales tax paid” = J (i.e. capital J, not lower-case j) 
Let Beth’s “sales tax paid” = B

J = 12,000*( j/100) 
B = 12,000*( k/100)

The question is, “How much more did John pay in sales tax than Beth paid? But let’s ask, “What is the question behind the question?” In other words, “What would we need to know in order to answer this question?” We need to know the difference between 12,000*( j/100) and 12,000*( k/100)

We need to know 12,000*(j - k)/100

So what we REALLY need to know is what j - k is equal to. The question behind the question is: What is j – k?

Now we can look at each statement.

Statement 1:

j = k+ 3
which means j - k = 3

SUFFICIENT

Statement 2:

j = (8/5)k

Can we find what j - k is equal to? No. That equation does not allow us to find the value of j – k.

NOT SUFFICIENT

Answer A

John and Beth each bought a used car at a purchase price of $12,000.

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John and Beth each bought a used car at a purchase price of $12,000.

Prep Toolkit

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